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Two elements x and y of a set S are said to be commutative under a binary operation * if they satisfy x*y=y*x. (1) Real numbers are commutative under addition x+y=y+x (2) and ...

A set U has compact closure if its set closure is compact. Typically, compact closure is equivalent to the condition that U is bounded.

If the parameters of a Lie group vary over a closed interval, them the Lie group is said to be compact. Every representation of a compact group is equivalent to a unitary ...

A topological space is compact if every open cover of X has a finite subcover. In other words, if X is the union of a family of open sets, there is a finite subfamily whose ...

A subset of a topological space which is compact with respect to the relative topology.

A function has compact support if it is zero outside of a compact set. Alternatively, one can say that a function has compact support if its support is a compact set. For ...

A compact surface is a surface which is also a compact set. A compact surface has a triangulation with a finite number of triangles. The sphere and torus are compact.

Inside a ball B in R^3, {rectifiable currents S in BL area S<=c, length partialS<=c} is compact under the flat norm.

Let suma_k and sumb_k be a series with positive terms and suppose a_1<=b_1, a_2<=b_2, .... 1. If the bigger series converges, then the smaller series also converges. 2. If ...

Let ||A|| be the matrix norm associated with the matrix A and |x| be the vector norm associated with a vector x. Let the product Ax be defined, then ||A|| and |x| are said to ...